2,737 research outputs found

### Inter-dimensional Degeneracies in van der Waals Clusters and Quantum Monte Carlo Computation of Rovibrational States

Quantum Monte Carlo estimates of the spectrum of rotationally invariant
states of noble gas clusters suggest inter-dimensional degeneracy in $N-1$ and
$N+1$ spacial dimensions. We derive this property by mapping the Schr\"odinger
eigenvalue problem onto an eigenvalue equation in which $D$ appears as a
continuous variable. We discuss implications for quantum Monte Carlo and
dimensional scaling methods

### Universal Dynamics of Independent Critical Relaxation Modes

Scaling behavior is studied of several dominant eigenvalues of spectra of
Markov matrices and the associated correlation times governing critical slowing
down in models in the universality class of the two-dimensional Ising model. A
scheme is developed to optimize variational approximants of progressively
rapid, independent relaxation modes. These approximants are used to reduce the
variance of results obtained by means of an adaptation of a quantum Monte Carlo
method to compute eigenvalues subject to errors predominantly of statistical
nature. The resulting spectra and correlation times are found to be universal
up to a single, non-universal time scale for each model

### Monte Carlo computation of correlation times of independent relaxation modes at criticality

We investigate aspects of universality of Glauber critical dynamics in two
dimensions. We compute the critical exponent $z$ and numerically corroborate
its universality for three different models in the static Ising universality
class and for five independent relaxation modes. We also present evidence for
universality of amplitude ratios, which shows that, as far as dynamic behavior
is concerned, each model in a given universality class is characterized by a
single non-universal metric factor which determines the overall time scale.
This paper also discusses in detail the variational and projection methods that
are used to compute relaxation times with high accuracy

### Surface and bulk transitions in three-dimensional O(n) models

Using Monte Carlo methods and finite-size scaling, we investigate surface
criticality in the O$(n)$ models on the simple-cubic lattice with $n=1$, 2, and
3, i.e. the Ising, XY, and Heisenberg models. For the critical couplings we
find $K_{\rm c}(n=2)=0.454 1655 (10)$ and $K_{\rm c}(n=3)= 0.693 002 (2)$. We
simulate the three models with open surfaces and determine the surface magnetic
exponents at the ordinary transition to be $y_{h1}^{\rm (o)}=0.7374 (15)$,
$0.781 (2)$, and $0.813 (2)$ for $n=1$, 2, and 3, respectively. Then we vary
the surface coupling $K_1$ and locate the so-called special transition at
$\kappa_{\rm c} (n=1)=0.50214 (8)$ and $\kappa_{\rm c} (n=2)=0.6222 (3)$, where
$\kappa=K_1/K-1$. The corresponding surface thermal and magnetic exponents are
$y_{t1}^{\rm (s)} =0.715 (1)$ and $y_{h1}^{\rm (s)} =1.636 (1)$ for the Ising
model, and $y_{t1}^{\rm (s)} =0.608 (4)$ and$y_{h1}^{\rm (s)} =1.675 (1)$ for
the XY model. Finite-size corrections with an exponent close to -1/2 occur for
both models. Also for the Heisenberg model we find substantial evidence for the
existence of a special surface transition.Comment: TeX paper and 10 eps figure

### Van der Waals clusters in the ultra-quantum limit: a Monte Carlo study

Bosonic van der Waals clusters of sizes three, four and five are studied by
diffusion quantum Monte-Carlo techniques. In particular we study the unbinding
transition, the ultra-quantum limit where the ground state ceases to exist as a
bound state. We discuss the quality of trial wave functions used in the
calculations, the critical behavior in the vicinity of the unbinding
transition, and simple improvements of the diffusion Monte Carlo algorithm.Comment: World Wide Web URL
http://www.phys.uri.edu/people/mark_meierovich/visual/Main.html contains an
informal presentation with color graphic

### Monte Carlo Optimization of Trial Wave Functions in Quantum Mechanics and Statistical Mechanics

This review covers applications of quantum Monte Carlo methods to quantum
mechanical problems in the study of electronic and atomic structure, as well as
applications to statistical mechanical problems both of static and dynamic
nature. The common thread in all these applications is optimization of
many-parameter trial states, which is done by minimization of the variance of
the local or, more generally for arbitrary eigenvalue problems, minimization of
the variance of the configurational eigenvalue.Comment: 27 pages to appear in " Recent Advances in Quantum Monte Carlo
Methods" edited by W.A. Leste

### Quantum Monte Carlo Methods in Statistical Mechanics

This paper deals with the optimization of trial states for the computation of
dominant eigenvalues of operators and very large matrices. In addition to
preliminary results for the energy spectrum of van der Waals clusters, we
review results of the application of this method to the computation of
relaxation times of independent relaxation modes at the Ising critical point in
two dimensions.Comment: 11 pages, 1 figur

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